English
Related papers

Related papers: Fast Unconstrained Optimization via Hessian Averag…

200 papers

This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random…

Optimization and Control · Mathematics 2022-05-16 Stefania Bellavia , Eugenio Fabrizi , Benedetta Morini

We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling…

Optimization and Control · Mathematics 2021-09-28 Raghu Bollapragada , Stefan M. Wild

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…

Optimization and Control · Mathematics 2019-05-15 Peng Xu , Fred Roosta , Michael W. Mahoney

We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and…

Optimization and Control · Mathematics 2023-06-26 Ahmet Alacaoglu , Hanbaek Lyu

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Optimization and Control · Mathematics 2020-05-29 Rohit Kannan , James Luedtke

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

Optimization and Control · Mathematics 2021-05-18 Jonathan Lacotte , Yifei Wang , Mert Pilanci

In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…

Optimization and Control · Mathematics 2023-03-01 Zijian Liu , Ta Duy Nguyen , Thien Hang Nguyen , Alina Ene , Huy Lê Nguyen

In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely on the asymptotic behavior of an inertial system combining geometric damping with temporal scaling. The convex function to minimize enters the…

Optimization and Control · Mathematics 2020-09-17 Hedy Attouch , Aicha Balhag , Zaki Chbani , Hassan Riahi

In this paper, we present a novel derivative-free optimization framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning involve settings…

Optimization and Control · Mathematics 2024-04-19 Raghu Bollapragada , Cem Karamanli , Stefan M. Wild

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Optimization and Control · Mathematics 2015-06-12 Euhanna Ghadimi , Iman Shames , Mikael Johansson

We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence…

Optimization and Control · Mathematics 2025-07-18 Zepeng Wang , Juan Peypouquet

In this paper, we present a detailed convergence analysis of a recently developed approximate Newton-type fully distributed optimization method for smooth, strongly convex local loss functions, called Network-GIANT, which has been…

Optimization and Control · Mathematics 2026-02-17 Souvik Das , Luca Schenato , Subhrakanti Dey

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

Machine Learning · Computer Science 2014-12-02 Jascha Sohl-Dickstein , Ben Poole , Surya Ganguli

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Optimization and Control · Mathematics 2018-05-01 James V. Burke , Frank E. Curtis , Adrian S. Lewis , Michael L. Overton , Lucas E. A. Simões

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

Optimization and Control · Mathematics 2023-05-31 Ilgee Hong , Sen Na , Michael W. Mahoney , Mladen Kolar

We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…

Optimization and Control · Mathematics 2019-02-04 Olivier Fercoq , Ahmet Alacaoglu , Ion Necoara , Volkan Cevher

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

Machine Learning · Statistics 2015-06-11 Atsushi Nitanda

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…

Optimization and Control · Mathematics 2018-03-12 Andre Milzarek , Xiantao Xiao , Shicong Cen , Zaiwen Wen , Michael Ulbrich

Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…

Optimization and Control · Mathematics 2015-08-05 Thomas Furmston , David Barber

We present a finite-time analysis of two smoothed functional stochastic approximation algorithms for simulation-based optimization. The first is a two time-scale gradient-based method, while the second is a three time-scale Newton-based…

Machine Learning · Computer Science 2026-04-01 Kaustubh Kartikey , Shalabh Bhatnagar